Yup, a better fence may help. We just fenced in the back yard as we got a dog. Dad and I did the work. We didn't want chain link, or wood, and wanted something inexpensive. (My dog is a 9 year old bichon, so we are emore interested in keeping coyotes OUT than in keeping her IN.)

We got everything at Home Depot, and it looks like in this link.

http://www.purrfectfence.com/

See the middle photo? We didn't do the curved top - YET. But as I have 7 cats, we planned so that we CAN do that extra piece if we need to.

Just thought this may be helpful. If you and your husband are the DIY types, you will find this an easy project. Good luck!